What I mean is that just giving them super-powers doesn't make them feel like a fantasy race, it makes them feel like... I don't know, the X-men.
It's good to give a race a mechanical benefit (or disadvantage) to differentiate them and make them stick closer to whatever concept you have in mind... But if their culture behavior is basically "human, but can cast fireball twice a day", it feels bland.
Even "minor" physiological traits could (and would) have a huge impact on culture and behavior.
Imagine how different human society would be if we had darkvision, for example. Or extreme resistance/vulnerability to cold... Or if we were twice as large (or small) as we are.
Sadly, in D&D (especially 5e, in my admittedly limited experience with that edition) these things are most often treated as little more than minor bonuses and lesser game abilities, but rarely have any actual impact in how a race or society works...
I remember really enjoying Races of Eberron for 3.5 because it actually tried to give each race a culture and behavior that took their mechanical characteristics into consideration and tried to make sense.